When people face possible arrest and fines or imprisonment for just being out in public while drunk then this encourages people to drive home. Since driving takes less time it's easy for the person to think "if I drive I have less chance of getting caught."
This is not to say that people who are drunk in public should get to do what ever they want. If they start a fight they should be arrested or at least stopped just like a sober person would if they started a fight. If they are being loud and obnoxious in public they should receive a citation for disturbing the peace or at least a warning depending on what the policy would be towards a sober person doing the same.
This law may mean that you cant ever be intoxicated in public but is not enforced that way (at least here). If you are not drinking, disturbing others, or throwing a fit the cops wont stop you from walking home. Just do not do dumb things like attempt to eat in a restaurant or become a bother and you will be fine.